where \(ds^2_M\)  is the metric of the Gibbons-Hawking space [1]}, which is written as
\(ds^2_M&=&H^{-1}(d\psi +\chi )^2+Hds^2_{{\mathbb {E}}^3}, \\ds^2_{{\mathbb {E}}^3}&=&dx^2+dy^2+dz^2=dr^2+r^2(d\theta ^2+\sin ^2\theta d\phi ^2),\\\chi &=&\sum _{i=1}^nh_i \frac{r\cos \theta -z_i}{r_i}d\phi ,\\H&=&\sum _{i=1}^n\frac{h_i}{r_i}. \) 
